Aircraft: CESSNA 170
Phase of flight: Landing
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Loss Of Aircraft Control; Ground Event / Encounter Object; Ground Excursion Taxiway; Ground Excursion Runway

[The pilot] asked me to fly with him in his Cessna 170 from ZZZ1 to ZZZ where he was going to fly for a demonstrated waiver as the FAA took his medical because of [a health condition]. The flight from ZZZ1 to ZZZ [was] fine and uneventful. After landing at ZZZ; [the Pilot] flew three takeoffs and landings in his Cessna 170 satisfactorily to full stops and taxied back. We then taxied into [the FBO] and met with [the Examiner] from the FSDO; where he said that I would be PIC (Pilot in Command) since [the Pilot] did not have a medical. We taxied to Runway XX and did a normal takeoff whereupon he was directed to fly northeast for about 10 miles. [The Examiner] asked [the Pilot] to fly various places and positions; so he could ascertain his visual prowess which he showed to be fine. [The Examiner] also asked him to fly a practice emergency landing which was marginal.[The Examiner] seemed satisfied and directed [the Pilot] to fly back to ZZZ whereupon he joined a right downwind leg for Runway XX. The approach was satisfactory which put us on a short final for Runway XX. [The pilot] had kept mentioning doing a wheel landing but I saw that he was going too slow and flared a little high to do a wheel landing. In other words; had he done a three point landing; he probably would have been fine. Because of being slow and a little high; he did bounce on the main gear; which I saw would happen. But I wanted to let him recover from it by doing the simple [act of] putting the nose down to stop the next bounce. At that point he did not fix the issue; so I then intervened and put the nose down which put us in a level condition [and] stopped the porpoising action. All there was to do was let the plane continue straight ahead and allow the tail to come down into a three point configuration.When the tail came down; the plane started to turn right; to which I immediately applied full left rudder and brake which should have easily prevented the plane from going right at all. The plane continued to turn right in spite of full rudder and brake; which took us to the right of the runway and [to] the right side of the taxiway. I [then] realized [the pilot] was applying both brakes; which eliminated any chance of regaining steering control again. In all my many years [of] teaching conventional gear flying; I have never been unable to correct any plane moving left or right until that moment; where I realized that if the pilot in the left seat is applying both brakes; I lose any ability to correct the aircraft from the right seat - which; to this point; nobody had ever done before.As we went onto the taxiway having no ability to turn the plane; he headed straight for the taxiway lights and all I could think [of] was [that] he was going to hit the prop and damage the engine. After getting out of the airplane and looking; to my amazement; the prop did NOT strike any lights. Rather; the tire rolled over one of the breakaway taxi lights and the other two lights hit the bottom of the tail section that made a very small thumbnail dent. Realizing the aircraft was not damaged; we taxied back to [the FBO] and called the Airport Administrator to report the taxiway lights that had been damaged. Afterward; I spoke to [the Examiner] and related to him that with both brakes being applied; I simply had no ability to correct the airplane's path. If it had been him just pushing the wrong rudder or not enough rudder; I could have easily corrected the airplane's path and stayed on the center line of the runway.After wrapping up everything; we flew back to ZZZ1; whereupon landing he did start to the right again; but I hit full left rudder and brake which straightened the plane out. [It] surprised me especially considering [the pilot] has over 5;000 hours and a Commercial pilot's license. I asked him how much flying he had done since [a few months ago] to which he related to me... none. To the best of my knowledge these were the events that transpired that day and after reflecting on every detail I am writing this report. C170 flight instructor reported the inability to recover from the student's loss of control on landing; resulting in the aircraft inappropriately exiting the runway.